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Interpreting and Curve Fitting Temperature Data

 Activity Description Activity Guide Table

This activity uses actual temperature data to initiate an exploration of the connections between coefficients and graphs of sine equations. It is an extension of a lesson taught by Andy McFarland and further developed by Robin Ward, at the time students at the University of Virginia.

Mathematics Topics: This activity involves sine equations and their coefficients (amplitude, period, vertical shift, horizontal shift), curve fitting, and regression.

Mathematical Thinking: Students interpret scatterplots, and derive coefficients for "best fit" sine equations, numerically and graphically.

Technology: Graphing calculators are used to draw scatterplots, draw graphs of various sine curves, and calculate regression equations.

Sample Screen Shots:
Below are screenshots showing: (1) average monthly temperature data for 3 cities, and (2) a series of scatterplots of the Washington DC data illustrating a method to curve fit the data.

 Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr Washington, DC 54 64 73 77 75 68 57 46 37 34 36 45 54 Verhoyansk, Russia 5 32 54 57 48 36 5 -35 -53 -57 -48 -25 5 Buenos Aries 63 55 48 50 52 55 59 66 72 73 73 70 63

Figure 1. Average Monthly Temperature for Washington, Verhoyansk, and Buenos Aires

Figure 2. An Incremental Approach to Curve-Fitting the Washington data

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